The planar spectrum in U(N)-invariant quantum mechanics by Fock space methods: I. The bosonic case

Prompted by recent results on Susy-U(N)-invariant quantum mechanics in the large N limit by Veneziano and Wosiek, we have examined the planar spectrum in the full Hilbert space of U(N)-invariant states built on the Fock vacuum by applying any U(N)-invariant combinations of creation-operators. We present results about 1) the supersymmetric model in the bosonic sector, 2) the standard quartic Hamiltonian. This latter is useful to check our techniques against the exact result of Brezin et al. The SuSy case is where Fock space methods prove to be the most efficient: it turns out that the problem is separable and the exact planar spectrum can be expressed in terms of the single-trace spectrum. In the case of the anharmonic oscillator, on the other hand, the Fock space analysis is quite cumbersome due to the presence of large off-diagonal O(N) terms coupling subspaces with different number of traces; these terms should be absorbed before taking the planar limit and recovering the known planar spectrum. We give analytical and numerical evidence that good qualitative information on the spectrum can be obtained this way.Comment: 17 pages, 4 figures, uses youngtab.sty. Final versio

Equation of Motion for a Spin Vortex and Geometric Force

The Hamiltonian equation of motion is studied for a vortex occuring in 2-dimensional Heisenberg ferromagnet of anisotropic type by starting with the effective action for the spin field formulated by the Bloch (or spin) coherent state. The resultant equation shows the existence of a geometric force that is analogous to the so-called Magnus force in superfluid. This specific force plays a significant role for a quantum dynamics for a single vortex, e.g, the determination of the bound state of the vortex trapped by a pinning force arising from the interaction of the vortex with an impurity.Comment: 13 pages, plain te

Understanding stochastic perturbation theory: toy models and statistical analysis

The numerical stochastic perturbation method based on Parisi-Wu quantisationis applied to a suite of simple models to test its validity at high orders.Large deviations from normal distribution for the basic estimators aresystematically found in all cases (``Pepe effect''). As a consequence oneshould be very careful in estimating statistical errors. We present someresults obtained on Weingarten's ``pathological'' model where reliable resultscan be obtained by an application of the bootstrap method. We also present someevidence that in the far less trivial application to Lattice Gauge Theory asimilar problem should not arise at moderately high loops (up toO(\alpha^{10}))

Exact and semiclassical approach to a class of singular integral operators arising in fluid mechanics and quantum field theory

A class of singular integral operators, encompassing two physically relevant cases arising in perturbative QCD and in classical fluid dynamics, is presented and analyzed. It is shown that three special values of the parameters allow for an exact eigenfunction expansion; these can be associated to Riemannian symmetric spaces of rank one with positive, negative or vanishing curvature. For all other cases an accurate semiclassical approximation is derived, based on the identification of the operators with a peculiar Schroedinger-like operator.Comment: 12 pages, 1 figure, amslatex, bibtex (added missing label eq.11

A new computational technique for re-entry flow calculations based upon a shock-fitting technique for unstructured grids

An in-house developed, 2D/3D unstructured CFD solver has been extended to deal with a mixture of thermally perfect gases in chemical non-equilibrium. The Euler equations have been coupled with a state-to-state kinetic model for argon plasma. The spatial discretization uses compact stencil Residual Distribution Schemes and shock waves can be modelled using either shock-capturing or shock-fitting. Promising results have been obtained using the shock-fitting approach for a 2D hypersonic flow past the fore-body of a circular cylinder

On the definition of Quantum Free Particle on Curved Manifolds

A selfconsistent definition of quantum free particle on a generic curved manifold emerges naturally by restricting the dynamics to submanifolds of co-dimension one. PACS 0365 0240Comment: 8 p., phyzzx macropackag

Effects of 5-year experimental warming in the Alpine belt on soil Archaea: Multi-omics approaches and prospects

We currently lack a predictive understanding of how soil archaeal communities may respond to climate change, particularly in Alpine areas where warming is far exceeding the global average. Here, we characterized the abundance, structure, and function of total (by metagenomics) and active soil archaea (by metatranscriptomics) after 5-year experimental field warming (+1°C) in Italian Alpine grasslands and snowbeds. Our multi-omics approach unveiled an increasing abundance of Archaea during warming in snowbeds, which was negatively correlated with the abundance of fungi (by qPCR) and micronutrients (Ca and Mg), but positively correlated with soil water content. In the snowbeds transcripts, warming resulted in the enrichment of abundances of transcription and nucleotide biosynthesis. Our study provides novel insights into possible changes in soil Archaea composition and function in the climate change scenario

The amyloidogenic potential and behavioral correlates of stress

Observations of elevated basal cortisol levels in Alzheimer's disease (AD) patients prompted the hypothesis that stress and glucocorticoids (GC) may contribute to the development and/or maintenance of AD. Consistent with that hypothesis, we show that stress and GC provoke misprocessing of amyloid precursor peptide in the rat hippocampus and prefrontal cortex, resulting in increased levels of the peptide C-terminal fragment 99 (C99), whose further proteolytic cleavage results in the generation of amyloid-beta (Abeta). We also show that exogenous Abeta can reproduce the effects of stress and GC on C99 production and that a history of stress strikingly potentiates the C99-inducing effects of Abeta and GC. Previous work has indicated a role for Abeta in disruption of synaptic function and cognitive behaviors, and AD patients reportedly show signs of heightened anxiety. Here, behavioral analysis revealed that like stress and GC, Abeta administration causes spatial memory deficits that are exacerbated by stress and GC; additionally, Abeta, stress and GC induced a state of hyperanxiety. Given that the intrinsic properties of C99 and Abeta include neuroendangerment and behavioral impairment, our findings suggest a causal role for stress and GC in the etiopathogenesis of AD, and demonstrate that stressful life events and GC therapy can have a cumulative impact on the course of AD development and progression.CC and IS were supported by stipends from the Max Planck Society and EU Marie Curie Training Fellowships (at University College London, UK). The collaboration between the German and Portuguese laboratories was supported through the German–Portuguese Luso-Alemas Program (DAAD/GRICES). This study was conducted within the framework of the EU-supported integrated project ‘CRESCENDO’ (Contract FP6-018652)

Vector coherent state representations, induced representations, and geometric quantization: I. Scalar coherent state representations

Coherent state theory is shown to reproduce three categories of representations of the spectrum generating algebra for an algebraic model: (i) classical realizations which are the starting point for geometric quantization; (ii) induced unitary representations corresponding to prequantization; and (iii) irreducible unitary representations obtained in geometric quantization by choice of a polarization. These representations establish an intimate relation between coherent state theory and geometric quantization in the context of induced representations.Comment: 29 pages, part 1 of two papers, published versio

A negative mass theorem for surfaces of positive genus

We define the "sum of squares of the wavelengths" of a Riemannian surface (M,g) to be the regularized trace of the inverse of the Laplacian. We normalize by scaling and adding a constant, to obtain a "mass", which is scale invariant and vanishes at the round sphere. This is an anlaog for closed surfaces of the ADM mass from general relativity. We show that if M has positive genus then on each conformal class, the mass attains a negative minimum. For the minimizing metric, there is a sharp logarithmic Hardy-Littlewood-Sobolev inequality and a Moser-Trudinger-Onofri type inequality.Comment: 8 page